2024/07/02 by Apostolov, Vestislav, Lahdili, Abdellah, Nitta, Yasufumi
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2407.01871
Using the Yau-Tian-Donaldson type correspondence for v-solitons established by Han-Li, we show that a smooth complex n-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than 2(n+1). Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal Kähler metrics on Fano manifolds. An extension of this correspondence to v-solitons is also obtained.